Performance analysis of PSK systems in the presence of slow fading, imperfect carrier phase recovery, and AWGN

Using Fourier series expansion and associated Legendre functions, the average bit error probability (BEP) of the binary and quaternary phase shift keying (BPSK and QPSK, respectively) on a single channel (no diversity) in the presence of different kinds of slow fading channels (Rayleigh, Nakagami-m, and Rician), phase recovery error, and additive white Gaussian noise has been evaluated. The detection loss and phase precision for both of BPSK and QPSK have been calculated. The series expressions of the average BEP proposed in this study are found to be converged with reasonable number of terms. The accuracy of the results is verified by computer simulation. The main contribution relies on the integral definition of the associated Legendre functions, which leads to BEP expressions involving associated Legendre functions of the first and second kinds. Although the approach is devoted for the PSK systems, it can be extended easily to other modulation schemes and noise impairments.